Related papers: Detecting random walks on graphs with heterogeneou…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
We consider the problem of deciding, based on a single noisy measurement at each vertex of a given graph, whether the underlying unknown signal is constant over the graph or there exists a cluster of vertices with anomalous activation. This…
We describe the full exit boundary of random walks on homogeneous trees, in particular, on the free groups. This model exhibits a phase transition, namely, the family of Markov measures under study loses ergodicity as a parameter of the…
In recent years, protocols that are based on the properties of random walks on graphs have found many applications in communication and information networks, such as wireless networks, peer-to-peer networks and the Web. For wireless…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
The task of \emph{community detection} in a graph formalizes the intuitive task of grouping together subsets of vertices such that vertices within clusters are connected tighter than those in disparate clusters. This paper approaches…
The node2vec random walk is a non-Markovian random walk on the vertex set of a graph, widely used for network embedding and exploration. This random walk model is defined in terms of three parameters which control the probability of,…
In the study of small and large networks it is customary to perform a simple random walk, where the random walker jumps from one node to one of its neighbours with uniform probability. The properties of this random walk are intimately…
Analyzing the mixing time of random walks is a well-studied problem with applications in random sampling and more recently in graph partitioning. In this work, we present new analysis of random walks and evolving sets using more…
The change detection problem is to determine if the Markov network structures of two Markov random fields differ from one another given two sets of samples drawn from the respective underlying distributions. We study the trade-off between…
Let $X$ be the constrained random walk on $\mathbb{Z}_+^d$ $d >2$, having increments $e_1$, $-e_i+e_{i+1}$ $i=1,2,3,...,d-1$ and $-e_d$ with probabilities $\lambda$, $\mu_1$, $\mu_2$,...,$\mu_d$, where $\{e_1,e_2,..,e_d\}$ are the standard…
Inference and hypothesis testing are typically constructed on the basis that a specific model holds for the data. To determine the veracity of conclusions drawn from such data analyses, one must be able to identify the presence of the…
Graphlets are induced subgraph patterns and have been frequently applied to characterize the local topology structures of graphs across various domains, e.g., online social networks (OSNs) and biological networks. Discovering and computing…
We consider the "searching for a trail in a maze" composite hypothesis testing problem, in which one attempts to detect an anomalous directed path in a lattice 2D box of side n based on observations on the nodes of the box. Under the signal…
We consider a model where a signal (discrete or continuous) is observed with an additive Gaussian noise process. The signal is issued from a linear combination of a finite but increasing number of translated features. The features are…
Dynamic systems characterized by diversified evolutions are not only more flexible, but also more resilient to attacks, failures and changing conditions. This article addresses the quantification of the diversity of non-linear transient…
We introduce the notion of a "random basic walk" on an infinite graph, give numerous examples, list potential applications, and provide detailed comparisons between the random basic walk and existing generalizations of simple random walks.…
We explore the use of machine-learning techniques to detect quantum speedup in random walks on graphs. Specifically, we investigate the performance of three different neural-network architectures (variations on fully connected and…
We derive a lower bound for the probability that a random walk with i.i.d.\ increments and small negative drift $\mu$ exceeds the value $x>0$ by time $N$. When the moment generating functions are bounded in an interval around the origin,…
The problem of a restricted random walk on graphs which keeps track of the number of immediate reversal steps is considered by using a transfer matrix formulation. A closed-form expression is obtained for the generating function of the…